A Polar-Metric-Based Evolutionary Algorithm.

Area of Science:

• Computational intelligence
• Optimization algorithms
• Evolutionary computation

Background:

• Multi- and many-objective optimization problems (MOPs and MaOPs) are challenging for traditional evolutionary algorithms.
• Convergence and diversity degrade rapidly as the number of objectives increases, especially for Pareto-dominance-based methods.
• Existing non-Pareto-dominance-based algorithms offer alternatives but have limitations.

Purpose of the Study:

• To propose a novel polar-metric (p-metric)-based evolutionary algorithm (PMEA) for solving MOPs and MaOPs.
• To introduce a dynamic adjustment mechanism for the p-metric's direction vectors.
• To evaluate PMEA's performance against state-of-the-art algorithms.

Main Methods:

• Development of the Polar-Metric-based Evolutionary Algorithm (PMEA).
• Implementation of a two-phase selection strategy combining non-dominated sorting and p-metric.
• Dynamic adjustment of p-metric direction vectors.
• Comparative experimental analysis using three performance metrics, including the p-metric.

Main Results:

• PMEA demonstrates promising performance across a range of MOPs and MaOPs.
• The proposed algorithm shows competitive convergence and diversity preservation.
• Empirical results indicate PMEA's effectiveness compared to six state-of-the-art evolutionary algorithms.

Conclusions:

• PMEA offers a viable and effective approach for tackling complex multi- and many-objective optimization problems.
• The p-metric, with dynamic direction vector adjustment, contributes to improved performance.
• PMEA represents a significant advancement in evolutionary algorithms for high-dimensional optimization.